Theorem: Equal Lengths of Tangents from External Point
Practice Quiz
Q1. What is the relationship between two tangents drawn from an external point to a circle?
✔ The theorem states that tangents from an external point are equal.
Q2. If the radius is 3 cm and tangent length is 4 cm, what is the distance from center to point P?
✔ Using Pythagoras theorem: sqrt(3^2 + 4^2) = 5.
Q3. What is the angle between the radius and the tangent at the point of contact?
✔ The radius is always perpendicular to the tangent at the point of contact.
Show transcript
[Slide 1] Visualizing Tangents from a Point
Welcome students. Today we explore why tangents from one external point are always equal. Think of wrapping a string around a circle from outside.
[Slide 2] The Tangent Length Theorem
Mathematically, if P is outside the circle, lengths PA and PB are identical. We prove this using RHS congruence rule in triangles. This theorem simplifies many geometry problems significantly.
[Slide 3] Solving a Numerical Problem
Let radius be three cm and tangent be four cm. We need hypotenuse OP. Square both sides and add them together carefully.
[Slide 4] Avoiding Calculation Errors
Students often mix up the radius and the tangent value. Remember the angle at contact is ninety degrees always. This ensures you apply Pythagoras correctly every time.
[Slide 5] Key Takeaways Summary
Remember the main rule and apply Pythagoras theorem correctly. This concept is crucial for board exam questions. Practice similar problems to build confidence quickly.